CN106772351B - Kalman filter method based on the memory of limited step - Google Patents
Kalman filter method based on the memory of limited step Download PDFInfo
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- CN106772351B CN106772351B CN201611030384.7A CN201611030384A CN106772351B CN 106772351 B CN106772351 B CN 106772351B CN 201611030384 A CN201611030384 A CN 201611030384A CN 106772351 B CN106772351 B CN 106772351B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/415—Identification of targets based on measurements of movement associated with the target
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- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
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- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention discloses a kind of kalman filter methods based on the memory of limited step, mainly solve the problems, such as that target following accuracy is low with stability in the prior art.Its technical solution is: obtaining the preceding N step state and state covariance of targetpath by traditional kalman filter method；Recall N step backward by current state, obtains the reference state of targetpath；The mobility of target is judged according to reference state, if generation is motor-driven, the speed of previous frame filtering is corrected；The validity currently measured is judged further according to reference state, if in vain, to new breath plus a weight less than 1, obtaining new new breath；One-step prediction covariance is obtained according to the state covariance of last moment, then calculates gain matrix；Current state is updated according to predicted state and gain matrix and new new breath；State covariance is updated according to one-step prediction covariance and gain matrix, completes target following.The present invention improves the accuracy and stability of target following, can be used for radar data processing.
Description
Technical field
The invention belongs to radar data processing technology fields, relate generally to the tracking filtering technique of microinching target, can
For the tenacious tracking to ground and sea-surface target.
Background technique
Radar is the process of tracking filter to the tracking of moving target, this is the core content of radar tracking, its work
With being that target state is made an estimate and predicted.The task of tracking is that the movement of target is established by related and filtering processing
Track.Radar system assesses target according to the estimation and prediction made during establishing target trajectory to target state
The security postures of movement and the safe effect of mobility.Therefore, the superiority and inferiority of radar tracking link working performance directly influences thunder
Up to the security effectiveness of system.
In view of important function of the target following in enhancement radar performance, various countries are non-always in dual-use equal fields
Often pay attention to developing this Radar Technology.Maneuvering target tracking theory has a great development, especially in the research of track algorithm
On, theory is even more to reach its maturity.In track algorithm, main linear autoregression filtering, two o'clock extrapolation filtering, Wiener filtering,
Weighted linear regression, alpha-beta filtering and Kalman filtering, wherein Kalman filtering algorithm occupies in target following theory
Leading position.
Traditional standard Kalman filtering algorithm is that one kind iterates lowest mean square RLS filtering technique, is the position target
It sets, velocity and acceleration describes the variation of dbjective state by the kinetics equation of target as dbjective state vector, utilizes
The calculation method of recursion estimates the state of target, to establish the track of target.Though Kalman filtering algorithm has convergence rate
Fastly, the small feature of operand.But this method common problem is exactly that tracking error is big, and tracking result may not restrain even
Have lose target situation, i.e., it stability it is not high.
Summary of the invention
It is an object of the invention to be directed to the deficiency of traditional standard Kalman filtering algorithm, propose a kind of based on limited step
The kalman filter method of memory improves the accuracy and stability of target following to reduce tracking error.
Realize the object of the invention technical solution, include the following:
(1) filter state is walked according to the preceding N of known target trackAnd predicted stateAnd
State covariance P (k-1 | k-1), N step is recalled backward according to the current state of targetpath, obtains the reference state of targetpathWherein, k=1,2 ..., N indicate the moment；
(2) according to the reference state of targetpathIt is motor-driven to judge whether target occurs:
2a) according to reference stateTo current time predicted stateDisplacement a and current
Moment predicted stateTo the displacement c of state quantity measurement Z (k), the angle theta between the two displacements is calculated:
Wherein, the inner product of<a, c>between expression a and c.
2b) to judge whether target occurs according to angle, θ motor-driven:
IfIt then indicates to measure within the scope of ± 45 ° of current goal track direction, target is not sent out
Life is dynamic, directly execution step (4)；
IfIt is motor-driven then to indicate that target has occurred, a weight w is added to the speed currently measured at this timeXWith
To last moment, the speed of filtering adds a weight wZ:
2c) according to the weight w of the speed currently measuredXWith the weight w of the speed of last moment filteringZCorrect last moment
Filtering, obtain updated filteringTo obtain updated predictionFurther according to current
The prediction at moment calculates the measurement of current time prediction
(3) according to the reference state of targetpathThe current reliability for measuring Z (k) of judgement:
3a) according to reference stateTo current time predicted stateDisplacement a and reference
StateTo the displacement b of state quantity measurement Z (k), the angle α between the two displacements is calculated:
Wherein, the inner product of<a, b>between expression a and b；
3b) according to the current measurement for measuring Z (k) and current predictiveObtain current new breath v (k):
The current reliability for measuring Z (k) 3c) is judged according to angle [alpha]:
If α >=0 cos, then it represents that current to measure reliably；
If α < 0 cos, then it represents that it is unreliable currently to measure, and to current new breath v (k) plus a weight w, obtains new new breath
V'(k), wherein w < 1；
(4) one-step prediction covariance P (k | k-1) is obtained according to the state covariance P of last moment (k-1 | k-1), in turn
Calculate current gain matrix G (k)；
(5) according to current predictive stateWith gain matrix G (k) and new new breath v'(k), when updating current
The filter state at quarter
(6) according to one-step prediction covariance P (k | k-1) and gain matrix G (k), current state covariance matrix P (k is updated
|k)。
The present invention has the advantage that compared with existing traditional kalman filter method
1. the present invention target occur it is motor-driven when, amendment is weighted to the speed of previous frame filter state, avoid with
Track result does not restrain the case where even target is lost；
2. the present invention judges the reliability currently measured by the way that targetpath to be recalled to N step backward, for insecure
It measures again by making it meet the requirement of reliability current new breath plus a weight less than 1, to substantially reduce tracking
Error；
3. the present invention makes the accuracy and stability of target following using the kalman filter method remembered based on limited step
It is greatly improved.
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below in conjunction with embodiment and
The invention will be further described for attached drawing.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is to measure reliability in the present invention to judge schematic diagram；
Fig. 3 is the simulation result diagram with traditional kalman filter method processing interruption track；
Fig. 4 is the simulation result with the kalman filter method processing interruption track in the present invention based on the memory of limited step
Figure；
Fig. 5 is the simulation result diagram that continuous track is handled with traditional kalman filter method；
Fig. 6 is the simulation result that continuous track is handled with the kalman filter method based on the memory of limited step in the present invention
Figure；
Specific embodiment
Referring to Fig.1, realization step of the invention includes the following:
Step 1: obtaining the reference state of targetpath.
Filter state is walked by the preceding N that traditional kalman filter method obtains targetpathAnd predicted stateAnd state covariance P (k-1 | k-1), wherein k=1,2 ..., N indicate the moment；
N step is recalled backward according to the current state of track, and obtained filter state is known as the reference state of targetpath
Step 2: according to the reference state of targetpathIt is motor-driven to judge whether target occurs.
Referring to Fig. 2, this step is implemented as follows:
2a) according to reference stateTo current time predicted stateDisplacement a and work as
Preceding moment predicted stateTo the displacement c of state quantity measurement Z (k), the angle theta between the two displacements is calculated:
Wherein, the inner product of<a, c>between expression a and c；
2b) to judge whether target occurs according to angle, θ motor-driven:
IfIt then indicates to measure within the scope of ± 45 ° of current goal track direction, target is not sent out
Life is dynamic, directly execution step 3；
IfIt is motor-driven then to indicate that target has occurred, gives the weight w of the speed currently measured respectively at this timeZ
With the weight w of the speed of last moment filteringX:
2c) according to the speed v currently measuredZWeight wZWith the speed v of last moment filteringXWeight wXAmendment upper one
The speed v of moment filteringX, obtain revised speed v'X:
v′X=wZ·vZ+wX·vX,
With revised speed v'XInstead of the speed v before amendmentX, obtain revised filteringIn turn
Update the prediction at current timeAre as follows:
Wherein, F (k-1) is state-transition matrix；
Further according to the prediction at current timeObtain the measurement of current time prediction
Wherein, H (k) is measurement matrix.
Step 3: according to the reference state of targetpathThe current reliability for measuring Z (k) of judgement.
3a) according to reference stateTo current time predicted stateDisplacement a and reference
StateTo the displacement b of state quantity measurement Z (k), the angle α between the two displacements is calculated:
Wherein, the inner product of<a, b>between expression a and b；
3b) according to the current measurement for measuring Z (k) and current time predictionObtain current new breath v (k):
The current reliability for measuring Z (k) 3c) is judged according to angle [alpha]:
If α >=0 cos, then it represents that current to measure reliably；
If α < 0 cos, then it represents that it is unreliable currently to measure, then to obtain new to current new breath v (k) plus a weight w
New breath v'(k), wherein w < 1.
Step 4: calculating one-step prediction covariance matrix and current gain matrix.
4a) according to the state covariance matrix P of last moment (k-1 | k-1) obtain one-step prediction covariance matrix P (k | k-
1):
P (k | k-1)=F (k-1) P (k-1 | k-1) FT(k-1),
Wherein, FTIt (k-1) is the transposition of state-transition matrix F (k-1).
Current gain matrix G (k) 4b) is calculated according to one-step prediction covariance matrix P (k | k-1):
G (k)=P (k | k-1) HT(k)(H(k)P(k|k-1)HT(k))-1,
Wherein, HT(k) transposition for being measurement matrix H (k), (H (k) P (k | k-1) HT(k))-1For H (k) P (k | k-1) HT(k)
It is inverse.
Step 5: updating the filter state at current time.
According to current predictive stateWith gain matrix G (k) and new new breath v'(k) Lai Gengxin current time
Filter state
Step 6: updating the state covariance matrix at current time.
According to one-step prediction covariance matrix P (k | k-1) and gain matrix G (k) Lai Gengxin current time state covariance
Matrix P (k | k):
P (k | k)=P (k | k-1)-G (k) H (k) P (k | k-1).
Effect of the invention can be further illustrated by the processing below to measured data:
1. experimental situation and condition:
Data transfer rate: 40s/ frame
Number of targets: 1
Range error: 10000m
Range rate error: 5m/s
In simulations, the frame number of two groups of data is respectively 122 frames and 347 frames.
2. experiment content and result:
Experiment 1, is filtered intermittent targetpath with traditional kalman filter method, as a result such as Fig. 3.
Experiment 2, is filtered intermittent targetpath with the method for the present invention, as a result such as Fig. 4.
Compare Fig. 3 and Fig. 4 as it can be seen that traditional kalman filter method filter value is larger with the fluctuation of measuring value, filtering
Effect is poor, especially bigger in the filtering error of track discontinuities.And filter value of the present invention is with the fluctuation very little of measuring value, filtering
Effect be improved significantly, the filtering error of track discontinuities is greatly reduced.
Experiment 3, is filtered continuous targetpath with traditional kalman filter method, as a result such as Fig. 5.
Experiment 4, is filtered continuous targetpath with the method for the present invention, as a result such as Fig. 6.
Compare by Fig. 5 and Fig. 6 as it can be seen that traditional kalman filter method filter value is larger with the fluctuation of measuring value, filtering is flat
Sliding effect is poor.And filter value of the present invention is with the fluctuation very little of measuring value, filtering effect be improved significantly.
To sum up, the present invention substantially reduces tracking error compared with traditional kalman filter method, improves the steady of tracking
It is qualitative.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (7)
1. the kalman filter method based on the memory of limited step, comprising:
(1) filter state is walked according to the preceding N that traditional kalman filter method obtains targetpathWith prediction shape
StateAnd state covariance P (k-1 | k-1), N step is recalled backward according to the current state of targetpath, obtains mesh
Mark the reference state of trackWherein, k=1,2 ..., N indicate the moment；
(2) according to the reference state of targetpathIt is motor-driven to judge whether target occurs:
2a) according to reference stateTo current time predicted stateDisplacement a and current time
Predicted stateTo the displacement c of state quantity measurement Z (k), the angle theta between the two displacements is calculated:
Wherein, < a, c > indicate the inner product between a and c；
2b) to judge whether target occurs according to angle, θ motor-driven:
IfIt then indicates to measure within the scope of ± 45 ° of current goal track direction, there is no machines for target
It is dynamic, directly execution step (4)；
IfIt is motor-driven then to indicate that target has occurred, a weight w is added to the speed currently measured at this timeXWith to upper
The one moment speed of filtering adds a weight wZ:
2c) according to the weight w of the speed currently measuredXWith the weight w of the speed of last moment filteringZCorrect the filter of last moment
Wave velocity obtains updated filteringTo obtain updated predictionFurther according to current
The prediction at moment calculates the measurement of current time prediction
v’X=wZ·vZ+wX·vX,
(3) according to the reference state of targetpathThe current reliability for measuring Z (k) of judgement:
3a) according to reference statePredicted state after to updateDisplacement a and reference stateTo the displacement b of state quantity measurement Z (k), the angle α between the two displacements is calculated:
Wherein, < a, b > indicate the inner product between a and b；
3b) according to the current measurement for measuring Z (k) and current predictiveObtain current new breath v (k):
The current reliability for measuring Z (k) 3c) is judged according to angle [alpha]:
If α >=0 cos, then it represents that current to measure reliably；
If cos α < 0, then it represents that it is unreliable currently to measure, and to current new breath v (k) plus a weight w, obtains new new breath v'
(k), wherein w < 1；
(4) one-step prediction covariance P (k | k-1) is obtained according to the state covariance P of last moment (k-1 | k-1), and then calculated
Current gain matrix G (k) out；
(5) according to current predictive stateWith gain matrix G (k) and new new breath v'(k), current time is updated
Filter state
(6) according to one-step prediction covariance P (k | k-1) and gain matrix G (k), current state covariance matrix P (k | k) is updated.
2. method according to claim 1, wherein obtain updated prediction prediction in step (2)Pass through
Following formula carries out:
Wherein, F (k-1) is state-transition matrix,For updated filtering.
3. method according to claim 1, wherein according to the prediction at current time in step (2)It calculates current
The measurement of moment predictionIt is carried out by following formula:
Wherein, H (k) is measurement matrix.
4. method according to claim 1, wherein according to the state covariance P of last moment (k-1 | k-1) in step (4)
One-step prediction covariance P (k | k-1) is obtained, is carried out by following formula:
P (k | k-1)=F (k-1) P (k-1 | k-1) FT(k-1)
Wherein, F (k-1) is state-transition matrix, FTIt (k-1) is the transposition of F (k-1).
5. method according to claim 1, wherein calculating current increase according to one-step prediction covariance P (k | k-1) in step (4)
Beneficial matrix G (k), is carried out by following formula:
G (k)=P (k | k-1) HT(k)(H(k)P(k|k-1)HT(k))-1
Wherein, H (k) is measurement matrix, HT(k) transposition for being H (k), (H (k) P (k | k-1) HT(k))-1For H (k) P (k | k-1) HT
(k) inverse.
6. method according to claim 1, wherein according to current predictive state in step (5)And gain matrix
G (k) and new new breath v'(k), update the filter state at current timeIt is carried out by following formula:
7. method according to claim 1, wherein according to one-step prediction covariance P (k | k-1) and gain square in step (6)
Battle array G (k), update current state covariance matrix P (k | k), it is carried out by following formula:
P (k | k)=P (k | k-1)-G (k) H (k) P (k | k-1)
Wherein, H (k) is measurement matrix.
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| CN108469609B (en) * | 2018-06-11 | 2022-02-18 | 成都纳雷科技有限公司 | Detection information filtering method for radar target tracking |
| CN109581353B (en) * | 2018-11-27 | 2022-11-25 | 北京信息科技大学 | Multi-target tracking method and system based on automobile radar |
| CN109990789A (en) * | 2019-03-27 | 2019-07-09 | 广东工业大学 | A kind of flight navigation method, apparatus and relevant device |
| CN111289965B (en) * | 2019-12-04 | 2023-06-16 | 南京长峰航天电子科技有限公司 | Multi-target radar rapid tracking method and system |
| CN111398948B (en) * | 2020-04-08 | 2021-12-10 | 成都汇蓉国科微系统技术有限公司 | Maneuvering small target track association method under strong clutter background |
| CN114740448B (en) * | 2022-06-10 | 2022-09-02 | 南京隼眼电子科技有限公司 | Target state estimation method and device for vehicle-mounted radar and storage medium |
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